{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:UEH54NYAA7QESZQGVDR374JEGJ","short_pith_number":"pith:UEH54NYA","canonical_record":{"source":{"id":"cond-mat/0612563","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-21T18:50:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"72dd28ae22a5ee9d87e6211fdaf4a63996f6d5e328ac7867c2a309c3f2880745","abstract_canon_sha256":"dcdda67de249b914fa9684a3823de6c5cbe66a1a604a73acd54464916a37c70d"},"schema_version":"1.0"},"canonical_sha256":"a10fde370007e0496606a8e3bff1243244fbc8b6ed38383b69642339c27d1daf","source":{"kind":"arxiv","id":"cond-mat/0612563","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0612563","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0612563v2","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0612563","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"UEH54NYAA7QE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"UEH54NYAA7QESZQG","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"UEH54NYA","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:UEH54NYAA7QESZQGVDR374JEGJ","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0612563","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-21T18:50:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"72dd28ae22a5ee9d87e6211fdaf4a63996f6d5e328ac7867c2a309c3f2880745","abstract_canon_sha256":"dcdda67de249b914fa9684a3823de6c5cbe66a1a604a73acd54464916a37c70d"},"schema_version":"1.0"},"canonical_sha256":"a10fde370007e0496606a8e3bff1243244fbc8b6ed38383b69642339c27d1daf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:38.539458Z","signature_b64":"MCdKmmUkdZh9AkzDRr8FYmPshAZtCqn5Xc01BL1uzvFATViA1rsGDkCtUGBbr0HQy8kyxroe9IB8v+wLG9UsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a10fde370007e0496606a8e3bff1243244fbc8b6ed38383b69642339c27d1daf","last_reissued_at":"2026-05-18T01:39:38.538661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:38.538661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0612563","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZ+ugfsRfbuTAC7gQw7Z0ZKMChU+V5JX/uyheTs6Cj0BXfZx280iYRgsVjj5wMQ4QcZ2gG1c+11cHa68haFQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:17:37.965060Z"},"content_sha256":"eee67d2f9b9c431c28f1f80df9053537767cd1c3939f420e58d5bfed8466996f","schema_version":"1.0","event_id":"sha256:eee67d2f9b9c431c28f1f80df9053537767cd1c3939f420e58d5bfed8466996f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:UEH54NYAA7QESZQGVDR374JEGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Survival probability of a diffusing particle constrained by two moving, absorbing boundaries","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alan J. Bray, Richard Smith","submitted_at":"2006-12-21T18:50:22Z","abstract_excerpt":"We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \\pm(L+ct). The result is Q(y,\\lambda) = \\sum_{n=-\\infty}^\\infty (-1)^n \\cosh(ny) \\exp(-n^2\\lambda), where y=cx/D, \\lambda = cL/D and D is the diffusion constant of the particle. The results may be extended to the case where the absorbing boundaries have different speeds. As an application, we compute the asymptotic survival probability for the trapping reaction A + B -> B, for evanesc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0612563","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+w3O9DxEmHbsBVuCCyB4At75Mhwe6oOalFtMqY59R0TvNioSmR01yvNnR1uOYSvO3f60P+F9152G8y5uySdoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:17:37.965713Z"},"content_sha256":"2bc62a93355c74373f1bfefed3b632f1e6a9fd606387508afd7c17290b3a8128","schema_version":"1.0","event_id":"sha256:2bc62a93355c74373f1bfefed3b632f1e6a9fd606387508afd7c17290b3a8128"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEH54NYAA7QESZQGVDR374JEGJ/bundle.json","state_url":"https://pith.science/pith/UEH54NYAA7QESZQGVDR374JEGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEH54NYAA7QESZQGVDR374JEGJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T23:17:37Z","links":{"resolver":"https://pith.science/pith/UEH54NYAA7QESZQGVDR374JEGJ","bundle":"https://pith.science/pith/UEH54NYAA7QESZQGVDR374JEGJ/bundle.json","state":"https://pith.science/pith/UEH54NYAA7QESZQGVDR374JEGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEH54NYAA7QESZQGVDR374JEGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:UEH54NYAA7QESZQGVDR374JEGJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dcdda67de249b914fa9684a3823de6c5cbe66a1a604a73acd54464916a37c70d","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-21T18:50:22Z","title_canon_sha256":"72dd28ae22a5ee9d87e6211fdaf4a63996f6d5e328ac7867c2a309c3f2880745"},"schema_version":"1.0","source":{"id":"cond-mat/0612563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0612563","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0612563v2","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0612563","created_at":"2026-05-18T01:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"UEH54NYAA7QE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"UEH54NYAA7QESZQG","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"UEH54NYA","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:2bc62a93355c74373f1bfefed3b632f1e6a9fd606387508afd7c17290b3a8128","target":"graph","created_at":"2026-05-18T01:39:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \\pm(L+ct). The result is Q(y,\\lambda) = \\sum_{n=-\\infty}^\\infty (-1)^n \\cosh(ny) \\exp(-n^2\\lambda), where y=cx/D, \\lambda = cL/D and D is the diffusion constant of the particle. The results may be extended to the case where the absorbing boundaries have different speeds. As an application, we compute the asymptotic survival probability for the trapping reaction A + B -> B, for evanesc","authors_text":"Alan J. Bray, Richard Smith","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-21T18:50:22Z","title":"Survival probability of a diffusing particle constrained by two moving, absorbing boundaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0612563","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:eee67d2f9b9c431c28f1f80df9053537767cd1c3939f420e58d5bfed8466996f","target":"record","created_at":"2026-05-18T01:39:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dcdda67de249b914fa9684a3823de6c5cbe66a1a604a73acd54464916a37c70d","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-21T18:50:22Z","title_canon_sha256":"72dd28ae22a5ee9d87e6211fdaf4a63996f6d5e328ac7867c2a309c3f2880745"},"schema_version":"1.0","source":{"id":"cond-mat/0612563","kind":"arxiv","version":2}},"canonical_sha256":"a10fde370007e0496606a8e3bff1243244fbc8b6ed38383b69642339c27d1daf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a10fde370007e0496606a8e3bff1243244fbc8b6ed38383b69642339c27d1daf","first_computed_at":"2026-05-18T01:39:38.538661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:38.538661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MCdKmmUkdZh9AkzDRr8FYmPshAZtCqn5Xc01BL1uzvFATViA1rsGDkCtUGBbr0HQy8kyxroe9IB8v+wLG9UsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:38.539458Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0612563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eee67d2f9b9c431c28f1f80df9053537767cd1c3939f420e58d5bfed8466996f","sha256:2bc62a93355c74373f1bfefed3b632f1e6a9fd606387508afd7c17290b3a8128"],"state_sha256":"930c97b70cb8ed7ca39fdd5d1c626f357ca1aed8c9c9e7feae3ef12ad5e75b76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufQJHIRi/9s3hRY+S4he+7fWcnTgHFSi0FPiVQJ6U5szT09YEqXl8RIIbl1eGDaHztECWwVq1aaPVbRufmjDDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:17:37.969363Z","bundle_sha256":"2d97b985ae5dcb3e093901a4c6886e1c9d51216cfef1581058dee230cbb63804"}}